Coherent anti-Stokes Raman scattering (CARS) microscopy has been used widely for noninvasive, label-free, three-dimensional chemical imaging of biological and polymeric samples. CARS microscopy is based on third-order nonlinear vibrational spectroscopy. The overall CARS signal is given by:|χ(ω)|2=|χNR|2+2χNRRe[χR(ω)]+|χR(ω)|2 
This signal contains a nonresonant background (NRB), arising from the nonresonant third-order susceptibility (χNR) and resonant component that is proportional to the square of the third-order resonant susceptibility (χR). The signal also contains a “cross term” proportional to the product of the two susceptibilities. The NRB is generated by all molecular species in the sample. The NRB is impulsive, and thus in phase with the excitation field, (i.e., is strictly real). The resonant component is the signal of interest; it is generated only when the frequency difference of excitation fields is close to a resonant vibrational frequency of a molecule in the sample. In contrast to the NRB, the resonant signal has a component that is in phase (real) and one that is out of phase (imaginary) with the excitation field.
There are two major classes of CARS microscopy—single frequency and broadband (or multiplex). Single frequency CARS approaches use two picosecond pulses tuned to a specific Raman mode, exciting only a single vibrational mode, to achieve fast data acquisition speed and high sensitivity. However, quantitative Raman spectrum analysis of complex media including biological samples generally requires information about many vibrational modes, and a wide range of frequency data at a single measurement. Multiplex and broadband CARS approaches have been demonstrated to provide a broad Raman spectrum at a single measurement by overlapping a narrowband picosecond pulse and a broadband pulse. Despite a relatively slow imaging speed, the multiplex measurement techniques show great advantages for analysis of crowded Raman spectra, e.g., in the fingerprint region (typically 400-2000 cm−1, and particularly 500-1800 cm−1), and in the C-H stretch region (2600-3200 cm−1).
The NRB can, and typically does, dominate the signal for single-frequency and broadband CARS approaches. The NRB can be sufficiently strong as to completely overwhelm weak resonant signals, leading to significant reduction in imaging contrast and sensitivity. Thus, the NRB has to be accounted for in signal processing or experimentally eliminated in order to realize the chemical imaging potential of CARS microscopy. In cases where the resonant component of the signal is of intermediate strength or stronger, it may be best to eliminate the NRB by experimental methods, and collect only the resonant component. On the other hand, while the presence of the NRB can obscure the resonant component in the raw CARS signal, the NRB actually amplifies the resonant signal through the presence of the cross term. Thus, when the resonant component is very weak, it may be advantageous to exploit the amplification of the resonant by the nonresonant component by allowing all or some fraction of the NRB to persist, collecting the full CARS signal and using a signal analysis method to separate the resonant and nonresonant contributions.
Several experimental approaches have been developed for reducing or eliminating the NRB contribution. These include frequency-modulation, epi-detection, polarization control, time-resolved, and interference CARS techniques. However, the frequency modulation technique is not currently available for coupling with broadband CARS microscopy. The epi-detection suppresses the contribution of bulk solvent but is applicable to only small features compared to the wavelength of the scattering light. Polarization control and time-resolved CARS techniques can attenuate resonant signals significantly.
Interferometric CARS offers the possibility of detecting an NRB-free CARS signal without attenuation. Interferometric detection methods can provide the real and imaginary response of the third-order nonlinear susceptibility χ(3) by measuring combined signal of a CARS field from the sample of interest and a well-controlled reference field. Heterodyne methods use a strong reference field (local oscillator) to enhance the resonant signal in addition to separating out the phase information. However, these reference fields are generally generated in a different medium. Under these circumstances it is generally very difficult to account for differential phase shift and differential chirp over a broad frequency range, and to remove phase jitter. Generating signal and reference fields in the same sample obviates these problems. Silberberg et al. as described in D. Oron, N. Dudovich, and Y. Silberberg, Phys. Rev. Lett. 90, (2003), have demonstrated single pulse CARS techniques where NRB is reduced by interfering adjacent narrow spectral components of a single ultrashort laser pulse using a pulse shaper. Since a spatial light modulator controls the whole frequency range of pump, Stokes, and probe fields, the number of elements in the spatial light modulator limits the product of spectral resolution and spectral range. Cicerone et al. as described in T. W. Kee, H. X. Zhao, and M. T. Cicerone, Opt. Express 14, 3631 (2006), have demonstrated a different approach to interferometric broadband CARS microscopy by mixing signal and reference fields that are generated by a spectrally narrow pulse and a broad pulse for pump light, respectively. However, in that approach, it was necessary to scan the phase of one of the probe beams, thereby increasing the data acquisition time.
Several signal analysis methods for accounting for NRB have recently been applied to broadband and multiplex CARS microscopy. These are described in E. M. Vartiainen, H. A. Rinia, M. Muller, and M. Bonn, Opt. Express 14, 3622 (2006); and S. H. Lim, A. G. Caster, and S. R. Leone, Opt. Lett. 32, 1332 (2007). The method of Lim et al. is based on Fourier transform spectral interferometry, and uses a sequence of steps that is equivalent, within an additive factor, to a Kramers-Kronig (KK) method described by Peterson and Knight in C. W. Peterson and B. W. Knight, J. Opt. Soc. Am. 63, 1238 (1973). In the approaches to KK transforms discussed above, the response of interest is assumed explicitly or implicitly to rise like a step function at time=0. However, such a step-function response could be realistic only when 1) the impulse triggering the signal is a delta function and 2) either the real and the imaginary component of the signal is entirely conjugate; or, if a nonconjugate part (e.g., a real-only component) does exist, it is spectrally flat. For CARS, none of these conditions are realized in practice; the probe pulse (the impulse triggering the response) typically has a temporal width similar to the Raman response time, and the complex resonant response is accompanied by a real nonresonant response, carrying a frequency-dependent amplitude that reflects the convolution of the pump and Stokes pulses.
Although various techniques have been described or proposed for reducing or accounting for nonresonant background (NRB) in coherent anti-Stokes Raman scattering (CARS) applications, a need remains for further reducing and/or accounting for such NRB.